R jogs at twice the speed of walking and runs at twice the speed of jogging. From his home to office, he covers half of the distance by walking and the rest by jogging. From his office to home, he covers half the distance jogging and the rest by running. What is his average speed (in km/h) in a complete round from his home to office and back home if the distance between his office and home is 10 km and he walks at the speed of 5 km/h?
\( \frac{90}{8} \)
\( \frac{60}{8} \)
\( \frac{60}{9} \)
\( \frac{80}{9} \)
If \(
k^{4} + \frac{1}{k^{4}} = 47
\) Then what is the value of \(
k^{3} + \frac{1}{k^{3}}
\)
The simplified form of (x + 2y)3 + (x - 2y)3 is:
The table given below shows the production of bike and truck by 5 companies.
| Companies | Bike | Truck |
| G | 800 | 600 |
| H | 550 | 400 |
| I | 600 | 300 |
| J | 350 | 700 |
| K | 400 | 750 |
What is the ratio of the production of truck by company H and I together to the production bike by company J and K together?
If \(
\sin \theta + \cos \theta = \frac{\sqrt{3} - 1}{2\sqrt{2}}
\) what is the value of tan θ + cot θ ?